1000=300t-16t^2

Solution for 1000=300t-16t^2 equation:

1000=300t-16t^2

We move all terms to the left:

1000-(300t-16t^2)=0

We get rid of parentheses

16t^2-300t+1000=0

a = 16; b = -300; c = +1000;
Δ = b2-4ac
Δ = -3002-4·16·1000
Δ = 26000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{26000}=\sqrt{400*65}=\sqrt{400}*\sqrt{65}=20\sqrt{65}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-20\sqrt{65}}{2*16}=\frac{300-20\sqrt{65}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+20\sqrt{65}}{2*16}=\frac{300+20\sqrt{65}}{32}
$